How long should you keep looking through your options before you settle on one?

The marriage problem in game theory can help us with the answer.

In the problem a man is seeking a wife. He has a number of potential girlfriends (we assume that they will all accept him should he propose). He can date each one in turn but once he has turned one down and moved on to the next girlfriend he can’t go back to an earlier girlfriend.

When should he stop searching and propose to his current girlfriend?

The answer is surprisingly simple. If there are a number of potential girlfriends, using the letter ‘n’ to represent the number, then he should reject the first n divided by ‘e’ (e is a key number in mathematics and has a value of about 2.72). He should then accept the next girlfriend after that who is better than all the preceding ones. If none of them are better than all the earlier ones then he ends up with the last girlfriend.

This is his optimal strategy and he ends up with the best girlfriend as his wife about 37% of the time (actually with a probability of 1 divided by e).

For a bit of fun let’s think about how soon a man (or woman) should get married using this rule. Let’s assume that he is 16 and wants to get married sometime before he is 46. This gives him 30 years to find his optimum partner. According to the theory he should not settle down until at least 30 divided by 2.72 years have gone by. This works out to be 11 years, so he shouldn’t get married before he is 27 otherwise he has reduced his chance of finding his best wife!

Of course, plenty of people do marry before 27 and when the similar games are played in experiments people also tend to stop earlier than they should.

Today’s takeaway: Don’t settle too early. When you have lots of options it is better to keep looking for longer.

There is an important distinction in game theory between simultaneous and sequential games.

Simultaneous games

A simultaneous game is one in which the players effectively make their decisions at the same time. They don’t actually have to make their decisions at exactly the same time as long as each player doesn’t know the other player’s choice when they choose their own strategy.

An example is the Prisoner’s Dilemma, where the two players have to decide their strategy without knowing what the other player has chosen. Even though the police might not interview each of the prisoners at exactly the same time they are still making their decision without knowing what the other player has chosen.

Sequential games

A sequential game is one in which the players take alternate turns to make their choices.

An example is chess. When I am making my move I know what your last move was and can use that information to determine my own strategy.

It is important to know who is going to move first in a sequential game as their may be a first mover advantage, or even a first mover disadvantage.

Rock, paper, scissors

Rock, paper, scissors is played as a simultaneous because if it was sequential the second player would see the first player’s move and always beat it.

If the first player chooses paper, then the second player chooses scissors.

If the first player chooses rock, then the second player chooses paper.

If the first player chooses scissors, then the second player chooses rock.

The difference between a simultaneous and a sequential game is clear. As a sequential game the second player has the advantage, as a simultaneous game it is fair.

Kim Jong-Un is a new leader in a dangerous situation. Hopefully he’s read up on some game theory!

There are lots of ways to look at the North Korean situation through the lens of game theory and this post looks at what various commentators have been saying.

Evan Osnos has written in the New Yorker that Kim is a dangerous wildcard but that China will continue to support him because having him in charge is preferable to the Americans or South Koreans taking charge in North Korea.

Tyler Cowen looks at the situation from the American standpoint saying that they have to take the position they do in support of the South Koreans to give confidence to their other allies such as Israel. The Americans don’t really support South Korea that much but they use their support to send a message to others.

Don Rich also brings Israel into the analysis. He also raises the tricky problem of how Kim can keep the domestic support he gains from his aggressive stance if he then backs down. It is all made more difficult by cultural differences and the risk that Kim Jong-Un may not be acting rationally at all.

This brings me to the final article by Tim Worstall who says that in his experience of dealing with the North Koreans, including handing over £10,000 in cash to get a rail freight deal concluded, shows that they might just be crazier than anyone gives them credit for!

Having read these it is my view that China are the key to the situation. They support North Korea because they would not want to see the Americans occupy the land. It is this Chinese support that gives Kim the confidence to sabre-rattle so loudly without worrying about a US invasion, but equally they won’t want him to actually start a war which they would either have to get involved in or let him lose.